I have three weeks left on my current extension. Will BI…

Yes... they'll process it when there are 30 days or less until expiration... I do it all the time

Bro, some people are saying yes, but I clearly remember going in a week or two before it was due and getting scolded for it

Yes. Don't wait until the last day. Always go early. They don't care if you're early, but if you're late you pay a fine

You can extend at the airport on arrival, so I don't see three weeks ahead being a problem. Is this your first extension? If so, you can do it online. Remember, the first extension online is a visa waiver, not a visa.

In some places you can have an agent do your visa extension, and once you factor in transportation and time it's actually cheaper than doing it yourself. I used a nearby agent in Angeles for a couple of extensions. They charged 600 pesos, but I didn't have to go to BI and didn't pay express fees.